Question: Find the sum of the values of $x$ which satisfy $x^2 +1992x = 1993$.
Solution: This problem is immediate once you know the following fact:

For the equation $ax^2 + bx + c = 0$, the sum of the solutions of the equation is $-b/a$ and the product of the solutions is $c/a$.

In this case, $b = 1992$ and $a = 1$, so the sum of the solutions is $-b/a = \boxed{-1992}$.